Chapter 8, Problem 3Q

To determine

Whether a small force can ever exert a greater torque than a larger force.

Answer to Problem 3Q

Solution:

A small force can exert a greater torque than a larger force and it depends on the lever arm.

Explanation of Solution

Formula used:

  $\tau =F\times r$

Calculation:

Torque is the product of a force and the distance between the point where the force is applied and the torque is being considered (or lever arm)

i.e. $\tau =F\times r$

Consider two forces, $F_1$ and $F_2$ , such that $F_2=\frac{1}{2}{F}_1$ acting at points $r_1$ and $r_2$ away, such that $r_2=4r_1$

  ${\tau }_1=F_1\times r_1$

  $\begin{array}{c}{\tau }_2=F_2\times r_2\\ =\frac{1}{2}{F}_1\times 4r_1\\ =2\left(F_1\times r_1\right)\\ =2{\tau }_1\end{array}$

Despite $F_2$ being half of $F_1$ , the torque due to it is twice that of the torque produced by $F_1$ .

Conclusion:

Therefore, a smaller force can exert a greater torque than a larger force and it depends on the lever arm.